A249074 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A249074

Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

1, 4, 1, 6, 4, 1, 32, 14, 4, 1, 60, 72, 24, 4, 1, 384, 228, 120, 36, 4, 1, 840, 1392, 564, 176, 50, 4, 1, 6144, 4488, 3312, 1140, 240, 66, 4, 1, 15120, 31200, 14640, 6480, 2040, 312, 84, 4, 1, 122880, 104880, 97440, 37440, 11280, 3360, 392, 104, 4, 1, 332640

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + 2n/f(n-1,x), where f(0,n) = 1. (Sum of numbers in row n) = A249074(n) for n >= 0. (n-th term of column 1) = A087299(n) for n >= 1.

LINKS

Clark Kimberling, Rows 0..100, flattened

EXAMPLE

f(0,x) = 1/1, so that p(0,x) = 1

f(1,x) = (4 + x)/1, so that p(1,x) = 4 + x;

f(2,x) = (6 + 4 x + x^2)/(3 + x), so that p(2,x) = 6 + 4 x + x^2).

First 6 rows of the triangle of coefficients:

4 1

6 4 1

32 14 4 1

60 72 24 4 1

384 228 120 36 4 1